{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import softmax, sigmoid, numerical_diff,numerical_gradient,gradient_descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.31682708 0.69627909]\n"
     ]
    }
   ],
   "source": [
    "def init_network():\n",
    "    network = {}\n",
    "    network['W1'] = np.array([[0.1, 0.3, 0.5], [0.2, 0.4, 0.6]])\n",
    "    network['b1'] = np.array([0.1, 0.2, 0.3])\n",
    "    network['W2'] = np.array([[0.1, 0.4], [0.2, 0.5], [0.3, 0.6]])\n",
    "    network['b2'] = np.array([0.1, 0.2])\n",
    "    network['W3'] = np.array([[0.1, 0.3], [0.2, 0.4]])\n",
    "    network['b3'] = np.array([0.1, 0.2])\n",
    "    return network\n",
    "\n",
    "\n",
    "def forward(network, x):\n",
    "    W1, W2, W3 = network['W1'], network['W2'], network['W3']\n",
    "    b1, b2, b3 = network['b1'], network['b2'], network['b3']\n",
    "\n",
    "    a1 = np.dot(x, W1) + b1\n",
    "    z1 = sigmoid(a1)\n",
    "    a2 = np.dot(z1, W2) + b2\n",
    "    z2 = sigmoid(a2)\n",
    "    a3 = np.dot(z2, W3) + b3\n",
    "    return a3\n",
    "\n",
    "\n",
    "network = init_network()\n",
    "x = np.array([1.0, 0.5])\n",
    "y = forward(network, x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 数值微分的例子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x114788e20>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f1(x):\n",
    "    return 0.01*x**2 + 0.1 * x\n",
    "\n",
    "\n",
    "def tangent_line(f, x):\n",
    "    # 求x为*时的切线\n",
    "    d = numerical_diff(f, x)  # x为*时的导数\n",
    "    y = f(x) - d*x\n",
    "    return lambda t: d*t + y  # 切线方程\n",
    "\n",
    "\n",
    "x = np.arange(0.0, 20.0, 0.1)\n",
    "y = f1(x)\n",
    "\n",
    "tf = tangent_line(f1, 5)\n",
    "y2 = tf(x)\n",
    "\n",
    "tf1 = tangent_line(f1, 10)\n",
    "y3 = tf1(x)\n",
    "\n",
    "# 绘制函数图像\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, y2)\n",
    "plt.plot(x, y3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f2(x):\n",
    "    if x.ndim == 1:\n",
    "        return np.sum(x**2)\n",
    "    else:\n",
    "        return np.sum(x**2, axis=1)\n",
    "\n",
    "\n",
    "x0 = np.arange(-2, 2.5, 0.25)\n",
    "x1 = np.arange(-2, 2.5, 0.25)\n",
    "# X, Y = np.meshgrid(x, y) 代表的是将x中每一个数据和y中每一个数据组合生成很多点\n",
    "# 然后将这些点的x坐标放入到X中,y坐标放入Y中,并且相应位置是对应的\n",
    "# x = [1, 2]\n",
    "# y = [3, 4]\n",
    "# X, Y = np.meshgrid(x, y)\n",
    "# X, Y\n",
    "# (array([[1, 2],\n",
    "#         [1, 2]]),\n",
    "#  array([[3, 3],\n",
    "#         [4, 4]]))\n",
    "X, Y = np.meshgrid(x0, x1)\n",
    "# x.flatten()是把numpy对象x降低到一维，默认是按照行来降维的\n",
    "# 等同于x.flatten('A') 想要按照列的方向降维，格式为：x.flatten('F')\n",
    "X = X.flatten()\n",
    "Y = Y.flatten()\n",
    "# 求梯度\n",
    "grad = numerical_gradient(f2, np.array([X, Y]))\n",
    "plt.figure()\n",
    "plt.quiver(X, Y, -grad[0], -grad[1], angles=\"xy\", color=\"#666666\")\n",
    "plt.xlim([-2, 2])\n",
    "plt.ylim([-2, 2])\n",
    "plt.xlabel('x0')\n",
    "plt.ylabel('x1')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X1')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 用梯度法求 f(x0 + x1) = x0**2 + x1 ** 2 的最小值\n",
    "def f3(x):\n",
    "    return x[0] ** 2 + x[1] ** 2\n",
    "\n",
    "\n",
    "init_x = np.array([-3.0, 4.0])\n",
    "lr = 0.1\n",
    "step_num = 20\n",
    "x, x_history = gradient_descent(f3, init_x, lr, step_num)\n",
    "plt.plot([-5, 5], [0, 0], '--b')\n",
    "plt.plot([0, 0], [-5, 5], '--b')\n",
    "plt.plot(x_history[:, 0], x_history[:, 1], 'o')\n",
    "plt.xlim(-3.5, 3.5)\n",
    "plt.ylim(-4.5, 4.5)\n",
    "plt.xlabel(\"X0\")\n",
    "plt.ylabel(\"X1\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.13 ('d2l')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "6bdcd3dff61cfecb093f68bfbd67338d4a9739a04d65268bf3b66287b86a0a9e"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
